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91.
四元数体上Minkowski不等式与Bergstrom不等式 总被引:1,自引:0,他引:1
杨忠鹏 《新疆大学学报(理工版)》1999,16(1):32-39
我们对四元数体上自共轭半正定矩阵按广义Schur补给出了Bergstrom不等式的推广。然后应用自共轭半正定矩阵的Bergstrom不等式得到了Minkowski不等式,我们的结果修正了重行列不等式的一些错误。 相似文献
92.
We present robust and asymptotically optimal iterative methods for solving 2D anisotropic elliptic equations with strongly jumping coefficients, where the direction of anisotropy may change sharply between adjacent subdomains. The idea of a stable preconditioning for the Schur complement matrix is based on the use of an exotic non‐conformal coarse mesh space and on a special clustering of the edge space components according to the anisotropy behavior. Our method extends the well known BPS interface preconditioner [2] to the case of anisotropic equations. The technique proposed also provides robust solvers for isotropic equations in the presence of degenerate geometries, in particular, in domains composed of thin substructures. Numerical experiments confirm efficiency and robustness of the algorithms for the complicated problems with strongly varying diffusion and anisotropy coefficients as well as for the isotropic diffusion equations in the ‘brick and mortar’ structures involving subdomains with high aspect ratios. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
93.
The Nevalinna–Pick algorithm yields a continued fraction expansion of every Schur function, whose approximants are identified.
These approximants are quotients of rational functions which can be understood as the rational analogs of the Wall polynomials.
The properties of these Wall rational functions and the corresponding approximants permit us to obtain a Khrushchev’s formula
for orthogonal rational functions. An introduction to the convergence of the Wall approximants in the indeterminate case is
presented.
This work was partially realized during two stays of the second author at the Norwegian University of Science and Technology
(NTNU) financed respectively by Secretaría de Estado de Universidades e Investigación from the Ministry of Education and Science
of Spain and by the Department of Mathematical Sciences of NTNU. The work of the second author was also partially supported
by the Spanish grants from the Ministry of Education and Science, project code MTM2005-08648-C02-01, and the Ministry of Science
and Innovation, project code MTM2008-06689-C02-01, and by Project E-64 of Diputación General de Aragón (Spain). 相似文献
94.
M.F. Martínez-Serrano 《Applied mathematics and computation》2009,215(7):2733-2740
In this paper, we give an additive result for the Drazin inverse with its applications, we obtain representations for the Drazin inverse of a 2 × 2 complex block matrix having generalized Schur complement S=D-CADB equal to zero or nonsingular. Several situations are analyzed and recent results are generalized [R.E. Hartwig, X. Li, Y. Wei, Representations for the Drazin inverse of a 2×2 block matrix, SIAM J. Matrix Anal. Appl. 27 (3) (2006) 757-771]. 相似文献
95.
We prove that all irreducible representations of the bismash product have Frobenius–Schur indicator +1, where k is an algebraically closed field of characteristic 0. If n = p, a prime, we find all indicators for . We also study more general bismash products.
Both authors were supported by NSF grants DMS-07-01291 and DMS-04-01399. 相似文献
96.
Let M = ( A B C D ) (A and D are square) be a 2 × 2 block matrix over a skew field, where A is group invertible. Let S=D-CA#B denote the generalized Schur complement of M. We give the representations and the group invertibility of M under each of the following conditions:(1)S=0; (2) S is group invertible and CAπB=0, where Aπ=I-AA#. And the second result generalizes a result of C. Bu et al. [Appl. Math. Comput., 2009, 215: 132–139] 相似文献
97.
Won Keun Min 《Applied Mathematics Letters》2012,25(3):310-314
We introduce and study the concept of similarity between soft sets, which is an extension of the equality for soft set theory. We also introduce the concepts of conjunction parameter (α∧β) and disjunction parameter (α∨β) of ordered pair parameter 〈α,β〉 for soft set theory, and we investigate modified operations of soft set theory in terms of ordered parameters. 相似文献
98.
对x = (x1, x2,···, xn) ∈ (0,1)n 和 r ∈ {1, 2,···, n} 定义对称函数
Fn(x, r) = Fn(x1, x2,···, xn; r) =∏1≤i1∑j=1r(1+xi3/1- xi3)1/r,
其中i1, i2, ···, ir 是整数. 该文证明了Fn(x, r) 是(0,1)n 上的Schur凸、Schur乘性凸和Schur调和凸函数. 作为应用,利用控制理论建立了若干不等式. 相似文献
99.
关于循环矩阵逆平方根矩阵的计算 总被引:1,自引:0,他引:1
利用矩阵分块降阶的方法给出了计算循环矩阵逆平方根矩阵的两种方法.可以证明这两种算法与已有的方法相比,在减少运算量方面具有较大的优势. 相似文献
100.
A class of matrices, defined by a displacement rank property, is introduced. Completion and extension problems are studied for matrices in this class, under certain positivity constraints. The extension problem is reduced to a standard interpolation problem for Schur matrix valued functions. 相似文献